There are five domesticated species of chili peppers.
- Capsicum annuum includes many common varieties such as bell peppers, wax, cayenne, jalapeños, Thai peppers, chiltepin, and all forms of New Mexico chile.
- Capsicum frutescens includes malagueta, tabasco, piri piri, and Malawian Kambuzi.
- Capsicum chinense includes the hottest peppers such as the naga, habanero, Datil and Scotch bonnet.
- Capsicum pubescens includes the South American rocoto peppers.
- Capsicum baccatum includes the South American aji peppers.
Given the growth habit of your plant, the Species is most certainly Capsicum annuum. But that isn't really what you were after, you want to know the Cultivar.
Unfortunately, no one is going to be able to tell you 100% for sure what cultivar it is. There are just too many very similar cultivars out there. I will say that too me it doesn't look anything like a jalapeno, more like a de árbol or aji. You don't remember what sort of chili you took the seeds from or even where you bought it?
Have a look here and here for some incomplete lists of cultivars.